To solve this equation, we need to find the value of x that satisfies the equation.

First, we expand the left side of the equation using the formula for the cube of a binomial:

(x+2)^3 = x^3 + 3x^2(2) + 3x(2)^2 + 2^3
(x+2)^3 = x^3 + 6x^2 + 12x + 8

Now, we set this expression equal to 125:

x^3 + 6x^2 + 12x + 8 = 125

Subtracting 125 from both sides, we get:

x^3 + 6x^2 + 12x - 117 = 0

Now, we need to find the value of x that satisfies this equation. This can be done by factoring the equation or using numerical methods such as the Rational Root Theorem or graphing the equation.

After solving for x, we find that x = 3.

Therefore, the solution to the equation (x+2)^3 = 125 is x = 3.